Page "Josiah Willard Gibbs" Paragraph 31

where the sum in the last term is over the different chemical species.

By Legendre-transforming this expression, he defined the concepts of enthalpy and " free energy " ( now universally known as the " Gibbs free energy "), a thermodynamic potential which is especially useful to chemists since it determines whether a reaction will proceed spontaneously at a fixed temperature and pressure.

In the same way he also obtained what is now known as the " Gibbs – Duhem equation.